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StatisticsEssentials Of StatisticsCompute the standard deviation for the pretest and posttest scores that were used in problems 2.6 and 3.12. The scores are reproduced here. Taking into account all of the information you have on these variables, write a paragraph describing how the sample changed from test to test. What does the standard deviation add to the information you already had? Case Pretest Posttest A 8 12 B 7 13 C 10 12 D 15 19 E 10 8 F 10 17 G 3 12 H 10 11 I 5 7 J 15 12 K 13 20 L 4 5 M 10 15 N 8 11 O 12 20 2.6 S W A local youth service agency has begun a sex education program for teenage girls who have been referred by the juvenile courts. The girls were given a 20-item test for general knowledge about sex, contraception, and anatomy and physiology upon admission to the program and again after completion of the program. The scores of the first 15 girls to complete the program are as follows. Case Pretest Posttest Case Pretest Posttest A 8 12 I 5 7 B 7 13 J 15 12 C 10 12 K 13 20 D 15 19 L 4 5 E 10 8 M 10 15 F 10 17 N 8 11 G 3 12 O 12 20 H 10 11 3.12 S W Compute the median and mean for both the pretest and posttest for the test scores first presented in problem 2.6 and reproduced here. Interpret the statistics. Case Pretest Posttest A 8 12 B 7 13 C 10 12 D 15 19 E 10 8 F 10 17 G 3 12 H 10 11 I 5 7 J 15 12 K 13 20 L 4 5 M 10 15 N 8 11 O 12 20BuyFind*arrow_forward*

4th Edition

HEALEY + 1 other

Publisher: Cengage Learning,

ISBN: 9781305093836

Chapter 4, Problem 4.6P

Textbook Problem

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Compute the standard deviation for the pretest and posttest scores that were used in problems 2.6 and 3.12. The scores are reproduced here. Taking into account all of the information you have on these variables, write a paragraph describing how the sample changed from test to test. What does the standard deviation add to the information you already had?

Case |
Pretest |
Posttest |

A | 8 | 12 |

B | 7 | 13 |

C | 10 | 12 |

D | 15 | 19 |

E | 10 | 8 |

F | 10 | 17 |

G | 3 | 12 |

H | 10 | 11 |

I | 5 | 7 |

J | 15 | 12 |

K | 13 | 20 |

L | 4 | 5 |

M | 10 | 15 |

N | 8 | 11 |

O | 12 | 20 |

**2.6**

Case |
Pretest |
Posttest |
Case |
Pretest |
Posttest |

A | 8 | 12 | I | 5 | 7 |

B | 7 | 13 | J | 15 | 12 |

C | 10 | 12 | K | 13 | 20 |

D | 15 | 19 | L | 4 | 5 |

E | 10 | 8 | M | 10 | 15 |

F | 10 | 17 | N | 8 | 11 |

G | 3 | 12 | O | 12 | 20 |

H | 10 | 11 |

**3.12**

Case |
Pretest |
Posttest |

A | 8 | 12 |

B | 7 | 13 |

C | 10 | 12 |

D | 15 | 19 |

E | 10 | 8 |

F | 10 | 17 |

G | 3 | 12 |

H | 10 | 11 |

I | 5 | 7 |

J | 15 | 12 |

K | 13 | 20 |

L | 4 | 5 |

M | 10 | 15 |

N | 8 | 11 |

O | 12 | 20 |

Expert Solution

To determine

**To find:**

The standard deviation for the pretest and posttest scores

**Given:**

The following table shows the data of pretest and posttest scores of the teenage girls.

Case | Pretest | Posttest |

A | 8 | 12 |

B | 7 | 13 |

C | 10 | 12 |

D | 15 | 19 |

E | 10 | 8 |

F | 10 | 17 |

G | 3 | 12 |

H | 10 | 11 |

I | 5 | 7 |

J | 15 | 12 |

K | 13 | 20 |

L | 4 | 5 |

M | 10 | 15 |

N | 8 | 11 |

O | 12 | 20 |

**Formula used:**

Let the data values be

The formula to calculate mean is given by,

The formula to calculate standard deviation is given by,

Where,

**Calculation:**

For pretest scores:

The size of the population is 15.

The mean is given by,

Substitute 15 for

Consider the following table of sum of squares,

Scores |
||

8 | 1.777769 | |

7 | 5.444429 | |

10 | 0.66667 | 0.444449 |

15 | 5.66667 | 32.11115 |

10 | 0.66667 | 0.444449 |

10 | 0.66667 | 0.444449 |

3 | 40.11107 | |

10 | 0.66667 | 0.444449 |

5 | 18.77775 | |

15 | 5.66667 | 32.11115 |

13 | 3.66667 | 13.44447 |

4 | 28.44441 | |

10 | 0.66667 | 0.444449 |

8 | 1.777769 | |

12 | 2.66667 | 7.111129 |

From equation

Square the both sides of the equation.

Proceed in the same manner to calculate

The standard deviation is given by,

From equation

Essentials Of Statistics

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